Continuity & Bernoulli worksheet with answers

Free printable Continuity & Bernoulli worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
12Q = 18 L/sv = 1 m/s, d = ?

A water line must carry 18 L/s. To limit noise and wear, the mean velocity should be 1 m/s. Find the inner pipe diameter d needed.

Q = 18 L/sv = 1 m/s
d = mm
2.Easy
12d1​ = 75 mm, v1​ = 0.75 m/sd2​ = 25 mm

Water flows at 0.75 m/s through the wide section of the pipe, which has a diameter of 75 mm. Find the volume flow rate Q.

d1 = 75 mmd2 = 25 mmv1 = 0.75 m/s
Q = L/s
3.Medium
12d1​ = 200 mm, p1​ = ?d2​ = 100 mm, p2​ = 200 kPa

Water flows at 28 L/s through a horizontal pipe that narrows from 200 mm to 100 mm. The pressure in the narrow section is 200 kPa. Ignoring losses, find the pressure p1 in the wide section.

Q = 28 L/sd1 = 200 mmd2 = 100 mmp2 = 200 kPaρ = 1000 kg/m³
p1 = kPa
4.Medium
12d1​ = 100 mm, p1​ = 240 kPad2​ = 75 mm, p2​ = ?

Water flows through a horizontal pipe that narrows from 100 mm to 75 mm. In the wide section the pressure is 240 kPa and the velocity is 2.25 m/s. Ignoring losses, find the pressure p2 in the narrow section.

d1 = 100 mmd2 = 75 mmp1 = 240 kPav1 = 2.25 m/sρ = 1000 kg/m³
p2 = kPa
5.Hard
C211 m5 md = 25 mmpC​ = ?

A hose with an inner diameter of 25 mm siphons water from an open tank. The highest point C of the hose is 1 m above the water surface, and the outlet (open to the air) is 5 m below the water surface. Ignore losses and take g = 9.81 m/s². Find the absolute pressure pC at point C. The atmospheric pressure is 101.3 kPa.

d = 25 mmzC = +1 mz2 = −5 mg = 9.81 m/s²patm = 101.3 kPa
pC = kPa
6.Hard
pair​ = 120 kPav = ?d = 40 mmh = 4 m

A closed water tank has compressed air above the water at a gauge pressure of 120 kPa. Water leaves through an opening with a diameter of 40 mm, 4 m below the water surface, into the open air. Ignoring losses, find the jet velocity v. Use g = 9.81 m/s².

pair = 120 kPa (gauge)h = 4 md = 40 mmρ = 1000 kg/m³g = 9.81 m/s²
v = m/s

Answer key

  1. 1. d = 151.4 mm
  2. 2. Q = 3.313 L/s
  3. 3. p1 = 206 kPa
  4. 4. p2 = 234.5 kPa
  5. 5. pC = 42.44 kPa
  6. 6. v = 17.85 m/s

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